## Vineet Loomba is teaching live on Unacademy Plus

DIFFERENTIAL EqUATIONS (DETAILED COURSE) JEE MAIN AND ADVANCED IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee -$ IIT-JEE Mentor Since 2010. -^ Doubts/Feedback in Comment Section * Comment other topics you want to revise. * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration V Definite Integration Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations Binomial Theorem V Straight Lines V Applications of Integrals V Circles (Detailed Course) V Probability MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola V Differential Equations Upcoming Courses next month: Statistics Matrices Determinants MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Solution: Solve sec2 d + tan (1-r tan )dr-0 ,. The given equation can be written as dr. Sec2 sec2 ie.tan'e dr tane l.e cosec2 d .cou dr Using the transformation MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Using the transformation cot -u, we get-cosec, d du the equation reduces to du dr whose IF. Hence, the solution of the given differential equation is given by i.e. u=r-1+Cer ie, cot -r-1 + Cer. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS N JEE MAIN AND ADVANCED (IIT-JEE) Bernoulli's equation dy Equations of the form dx + Py Q.yn, n 0 and n # 1 where P and Q are functions of x, is called Bernoulli's equation Divide by y 2. Put y-n+1 v. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) 2 , dy-y-y (Bernoulli's equation) Example Solve dx Solution. Dividing both sides by y2 1 dy 1 1 y2 dk xy x .(1) 1 dy dt Putting y = t : differential equation (1) becomes, dt 1 dt t 1 dt +--which is linear differential equation in dx X x MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dx General solution is x dx C -Inx C ER. VINEET LOOMBA (IIT RooRKEE) MATHEMATICS FOR IIT-JEE

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SELF PRACTICE PROBLEMS 2 Solve x (x2 + 1) y (1 - X2) + x2 Inx dx Ans: y2 (x2 + 1 + ce Ans: X y (c + y2) Ans: x1ny = e"(x-1) + c 3 Solve: ( +2y') X y dx dx MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

100% SUCCESS IN JEE MAIN AND ADVANCED Save . Save for this Course (Free) MOST IMPORTANT QUESTIONS IN MATHEMATICS JEE MAIN AND ADVANCED . Recommend Lessons (Like) PREPARED BY ER. VINEST LOOMSA ITIAN | IT-IEE MENTOR IT-FEE MATHS MADE CASY Rate and Review the Course . Comments . Sharing with friends 00:00 05:46 SURE SROT Success IEE MAlm AND ADVANCED CtIT-IEE) 91 likes 18 comments A Share HINDI Crash Course Maths (Hindi) Most Important Questions in IIT-JEE Mathematics (Chapter- Wise) Vineet Loomba Follow 11k Followers 5.0 (51 ratings) Edit review